20-CS-4003-001 Organization of Programming Languages Fall 2017
Lambda

Lambda calculus, Type theory, Formal semantics, Program analysis

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Lambda - Y Combinator

(define F
  (lambda (n)
    (if (zero? n)
        1
        (* n ((lambda (arg) 
                ((procedure procedure) arg)) (- n 1))))))
 -  In general, isn't
   (f arg)
identical to
   ((lambda (x) (f x)) arg) ?
The second statement is a little strange, though, because it makes you pass "arg" into a procedure so that the procedure which would be applied to it anyway is applied. Why do we want to do such a thing? Watch! This means that
   ((procedure procedure) (- n 1))
is the same as
   ((lambda (arg) ((procedure procedure) arg)) (- n 1))
and we substitute this into our current version of F to get the code to the left.